Question

The number of words, that can be formed by using all letters of the word DAUGHTER, if relative order of vowels and consonants remains same, are

• A. $2880$
• B. $6720$
• C. $720$
• D. $3600$

Answer 1

The correct option is C $720$

The given word consist of 8 different letters in which $3$ are vowels and $5$ are consonants.

The relative position of vowel and consonants remain same means that vowel can take place of vowel and consonants to take place of consonants.

Now the $3$ vowels can be arranged among themselves in $3!=3!2!1!=6$ ways

The $5$ consonants can be arranged among themselves in $5!=5!4!3!2!1!=120$ways

$\therefore$The total numbers of words that can be formed$=120\times 6=720$